Research Paper on Multivariate Garch Models

Introduction

In economic systems ARCH (the autoregressive conditional heteroskedasticity) model is a mathematical representation for time sequence data that illustrates the difference in the existing innovation as a fraction of the real size of the past time sequence's error terms (Virbickaite, Ausin and Galeano, 2015 Pg.14). Mostly the difference is associated with the squares of the past innovations. The ARCH model is efficient when the error difference in a duration sequence trails an AR (autoregressive) model. Whenever an ARMA (autoregressive moving average) model is unspecified for the error difference, then the formation becomes GARCH (generalized autoregressive conditional heteroskedasticity) model. The ARCH formation is primarily used in analyzing and shaping financial time sequences that show duration's varying volatile as well as volatile clusters (Hanif and Khan, 2017.pg.25). By utilizing multivariate GARCH formations, it is evident that economic volatility goes hand in hand within a period of market and commodities.

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It is significant to utilize multivariate formation systems to identify features of important experiential models contrary to using different univariate formations. From an economic perspective, multivariate GARCH paves the way for effective decision equipment in a variety of business environment including risk management, portfolio selection, asset pricing, hedging as well as option pricing. The models have helped many organizations to develop important skills that enabled them to utilize economic concepts from a financial point of view. This literature focuses on the importance of multivariate GARCH models, their limitations on practical use and their availability of software that is capable of estimating the models. The paper utilizes a literature review from an article Multivariate GARCH model: A survey by Bauwens, Sebastian, and Jeroen (2006).

Usefulness of Multivariate Model

MGARCH is useful in the study of the relationship between the co-volatiles and volatiles of various markets. The models are important in answering the question whether the volatility of the various markets is as a result of the volatility of a market (Allen, McAleer, Powell and Singh, 2015.pg.54). Additionally, the models answer the question on the volatility of a commodity whether it is transmitted to another commodity directly or indirectly. The models are useful in determining the shock on markets and the degree of the shock. MGARCH model investigates whether connections between commodities profit changes with time (Johansen and Juselius, 2017.Pg.35). Some scientists have utilized these formations to examine the effect of volatility in economic markets on perfect variables such as output growth rates and exports. Also, MGARCH formations are used in the calculation of period-varying enclosed quotients. It is also useful in the computation of return factors such as market profits in the financial commodity pricing formations where GARCH models approximate time variance coefficients.

Through approximated single-variate formation, investors identify the conditional profit distribution which enables them to foresee VaR (value-at-risk) from a short or long location. In general MGARCH models are useful in studying dataset in markets and consumer's research, quality assurance, process maximization, quality control as well as research development. These models are important in providing statistical approximation on the associations between diverse variables and show the correlation amongst them.

Limitations of Multivariate GARCH Models

MGARCH models utilize a high level of statistical data that makes them complex in computation, and they require mathematical programs which are capable of analyzing the data. Also, the results obtained from MGARCH model are hard to interpret, and many of them are attributed to assumptions which are difficult to prove. On the other hand, to acquire useful results, multivariate models require a massive sample data (Fengler and Herwartz, 2018 pg 40). Otherwise, the findings become meaningless due to various statistical errors. The main challenge in MGARCH formation is that it is limited to restrictive difference matrix that has to be affirmative definite and almost perfect at all time t. To achieve a positive definite for all periods, multiple assumptions must be created to constrain the variable's space.

MGARCH models are limited to multiple numerical methods for the approximation of copies that results from various assumptions used. Outcomes from MGARCH formations are not limited to leverage effects a situation that makes the results incorrect. On the other hand, some multivariate GARCH are not invariant in cases of linear transformation thus they remain in a single class if linear transformations are used. The models are limited to both temporal aggregation and marginalization processes in univariate cases (Wozniak, 2015. Pg.28).In the classes of fragile MGARCH, procedures are found under sequential aggregation.

Available Software for MGARCH

In the modern world, there are a few packages of software that are capable of approximating multivariate data. MGARCH models have invited multiple studies thus man software is under development to aid in the future empirical investigation (Asai, 2016.pg.21). Currently, there is diagnostic checking software used to minimize time used in computation and ensure accuracy is estimated for multivariate models. This software can conduct various diagnostic checkups such as portmanteau statistics, residual-based diagnostics, and Lagrange multiplier tests. Portmanteau statistics are utilized to distinguish ARCH influences. Residual-based diagnostics are performed to test the statistical importance of regression ratios. They are applied across commodities of homogeneous residuals. Finally, Lagrange multiplier tests are conducted to identify ARCH's effects since they utilize higher powered equipment as compared to portmanteau tests.

Conclusion

From the literature survey, GARCH is as a result of the assumptions of ARMA as the error of the difference. To conduct economic computations the utilization of mathematical models such as MGARCH is significant to illustrate the variation in time sequence data (Francq, Horvath and Zakoian, 2014.pg.43). MGARCH models are the most accurate formations in measuring time sequence errors through the knowledge provided by multivariate it is correct to say that economic volatilities move together throughout commodities and markets.

Reference List

Allen, D., McAleer, M.J., Powell, R.J. and Singh, A.K., 2015. A volatility impulse response analysis applying multivariate GARCH models and news events around the GFC.

Asai, M., 2016. Bayesian Analysis of General Asymmetric Multivariate GARCH Models and News Impact Curves. Journal of the Japan Statistical Society, 45(2), pp.129-144.

Fengler, M.R. and Herwartz, H., 2018. Measuring Spot Variance Spillovers when (Co) variances are Timevarying-The Case of Multivariate GARCH Models. Oxford Bulletin of Economics and Statistics, 80(1), pp.135-159.

Francq, C., Horvath, L. and Zakoian, J.M., 2014. Variance targeting estimation of multivariate GARCH models. Journal of Financial Econometrics, 14(2), pp.353-382.

Hanif, W. and Khan, M., 2017. Hedging Effectiveness of Commodities in the Stock Portfolio: Empirical Evidence from Pakistan Stock Exchange using Multivariate GARCH Models. South Asian Journal of Management Sciences (SAJMS), Iqra University, 11(2), pp.153-175.

Johansen, S. and Juselius, K., 2017. Direct and Spill-Over Effects of Exchange Rate Volatility on Inflation in Swaziland: An Application of the Multivariate GARCH Model. Research Bulletin Volume, 52(2), p.84.

Virbickaite, A., Ausin, M.C. and Galeano, P., 2015. Bayesian inference methods for univariate and multivariate GARCH models: A survey. Journal of Economic Surveys, 29(1), pp.76-96.

Wozniak, T., 2015. Testing causality between two vectors in multivariate GARCH models. International Journal of Forecasting, 31(3), pp.876-894.